• Find Critical numbers of functions
• Locate Local/Relative Minimums and Maximums (extrema on an open interval)
• Identify Absolute Minimums and Maximums (extrema on a closed interval)

Lab: The Numbers are Critical when it comes to Derivatives
Homework:  Read and Take Notes on 4.1 (p.203 - 208) and Do p. 209 # 1, 3, 6, 9, 12, 15, 18, 21, 24, 33, 42

PowerPoint: Critical Points of Derivatives:  Going to Extrema -  Student Notes
 PowerPoint

Homework:  Read and take notes on section 4.1 (p. 203 – 208) and do p. 210# 45, 51, 54, 61, 62, 67 - 74

Activity:  Exploring Graphing Functions and their derivatives.

Going to Extremes!

due today!Only 1 more movie after this one!

4.2 – Rolle's Theorem and the Mean Value Theorem (MVT)
By the end of this lesson you should be able to:

• Understand and use Rolle's Theorem
• Understand and use the Mean Value Theorem (MVT)

Homework:  Read and take notes on section 4.2 (p. 212 – 215) and 
Pick 6 from p. 216 #1-4, 5, 8,  10, 14, 15, 18, 19, 21, 24, 27, 30, 33, 34
And 6 from p. 216 # 35, 36, 39, 41, 44, 46, 51, 53, 63, 65, 66, 67, 79 - 82

 Need more help with Rolle's Theorem and the Mean Value Theorem?  Try the Visual Calculus  website

"The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance."
      -- E. Purcell and D. Varberg

Tuesday,
Dec. 1

4.3 – Increasing and Decreasing Functions and the First Derivative Test

By the end of this lesson you should be able to:

• Determine intervals on which a function is increasing or decreasing
• Apply the First Derivative Test to find relative extrema of a function

Homework:  Read and take notes on section 4.3 (p. 219 – 225) and

PICK 6 problems from p. 226 # 1, 6, 10, 17, 20, 23, 28, 31, 41, 88, 93 and 6 problems from Do p. 226 # 51, 54, 66-68, 71-73, 76, 101-106

going up the hill = increasing

Homework: 
Pick 8 more problems from 4.2 and 4.3 that you haven’t done yet.

going down the hill = decreasing

4.4 – Concavity and the Second Derivative Test

By the end of this lesson you should be able to:

• Determine intervals on which a function is concave up or concave down
• Find any points of inflection of the graph of a function
• Apply the Second Derivative Test to find relative extrema of a function

Homework:  Read and take notes on section 4.4 (p. 230 – 234) and do p. 235 # 6, 10, 15, 22, 25, 75, 80

FILL THIS CUP UP and it means concave UP - 2nd derivative is positive!

4.4 – Concavity and the Second Derivative Test
By the end of this lesson you should be able to:

• Determine intervals on which a function is concave up or concave down
• Find any points of inflection of the graph of a function
• Apply the Second Derivative Test to find relative extrema of a function

Homework:  Do p. 235 # 29, 35, 36, 42, 62, 67, 89-94

Watch this can of paint turn  UPSIDE DOWN and this means that it is concave down - the second derivative is negative!

due today!

Last Movie

4.5 – Limits at Infinity (revisited)
By the end of this lesson you should be able to:

• Determine (finite) limits at infinity.
• Determine the horizontal asymptotes, if any, of the graph of a function.
• Determine infinite limits at infinity.

Homework:  Read and take notes on section 4.5 (p. 238 – 244) and do p. 245 # 16, 30, 51, 59, 66, 69, 70, 95, 97, 102, 117-118

The ants are toting this apple
horizontally...

Can you find horizontal totes?

Practice
  
4.6 – A Summary of Curve Sketching

By the end of this lesson you should be able to:

• Analyze the graph of a function with and without technology- domain, range, increasing, decreasing, mins, maxs, inflection points, concavity, vertical and horizontal asymptotes.
• Sketch a graph of a function by examining domains ranges, first and second derivatives without a graphing calculator.

Homework:  Read and take notes on section 4.6 (p. 249 – 255) and do
p. 255 # 1-4, 10, 13, 16, 17, 69, 73, 74

4.6 – A Summary of Curve Sketching
By the end of this lesson you should be able to:

• Analyze the graph of a function with and without technology- domain, range, increasing, decreasing, mins, maxs, inflection points, concavity, vertical and horizontal asymptotes.
• Sketch a graph of a function by examining domains ranges, first and second derivatives without a graphing calculator.

Homework:  Do p. 256 # 22-24, 31-33, 87, 94 and Begin creating your Note card for the two day

Thursday,
Dec. 10

4.7 Optimization Problems

By the end of this lesson you should be able to:

• Solve applied minimum and maximum problems

Homework:  Read and take notes on section 4.7 (p. 259 – 264)
and do p. 265 # 2, 5, 17-19, 21, 26, 29.

This guy needs the factory running at maximum efficiency with minimum cost - that's OPTIMIZATION!

4.7 Optimization Problems

By the end of this lesson you should be able to:

• Solve applied minimum and maximum problems.

Homework:  Do p. 266 # 35, 39-42, 54-55, 59, 60  and begin work on the take-home test

Chapter 4 Review

Homework:  Finish the take home exam (due Wednesday)

With Notes

This Page was Updated:
02/14/2010 02:45 PM

 

Additions, Corrections,
Suggestions?
Send me your thoughts!
Nancy Powell
BHS Lead Teacher - Math